State-of-the-art cardiovascular disease (CVD) research presents novel, complex data-analytic challenges. This project will develop new statistical methods for such problems, motivated by the investigators' involvement in numerous CVD studies, that either break new ground, addressing issues for which no principled approaches exist, or that offer improvement over existing techniques. Many CVD studies seek to compare intervention-specific survival distributions using large observational databases. The objective of the first two aims is to develop new, optimal methods for estimating and comparing survival distributions in this setting, where the time-to-event out- come of interest may be censored, that take appropriate account of the confounding inherent in these data. The first aim is to derive optimal estimators for the survival distribution, the difference in treatment-specific survival distributions, and the hazard ratio for two treatments in a proportional hazards model. The estimators will rely on postulated models for the propensity of treatment, the censoring distribution, and the survival distribution as functions of patient covariates and will be doubly robust in the sense that they will be consistent for the true quantities even if subsets of these models are misspecified. In some settings, the data are obtained from vast registries where it is infeasible to collect on all subjects the detailed covariate information needed to adjust appropriately for confounding. A stratified sample that deliberately over-represents important subsets of the patient population may be obtained, from whom rich information on potential confounding variables is collected. The second aim is to develop such doubly robust estimators for the survival distribution under this complex sampling design. The goal of many CVD studies is to compare treatments on the basis of a composite time-to-event endpoint such as time to myocardial infarction or death (whichever comes first). However, some subjects may withdraw from the study before the composite endpoint may be ascertained, rendering it censored at the time of withdrawal. However, vital status for all subjects may be obtained at the end of the study from the national death indices, so that, for subjects who withdraw, additional information on one component of the composite is available. The third aim is to develop new methods for exploiting this information to obtain more precise estimators of and more powerful tests regarding treatment-specific survival distributions for the composite endpoint. A key challenge when linking administrative databases is the potential for information on intervention to be unreliable or conflicting; e.g., in a study to compare endoscopic vs. open vein graft harvesting in patients undergoing coronary artery bypass graft surgery, Medicare claims data may misclassify the technique used in some pro- portion of patients. The fourth aim is to develop improved methods for comparison of interventions based on a censored time-to-event outcome in this setting. Across all aims, the methods address problems both unique to CVD research and common in other chronic disease settings; thus, the latter will be broadly translatable across many disease areas.